Preparing for the Regents Examination Geometry, AK

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8 Draw a point. Draw an arc centering on the point. Draw two lines from the point intersecting the arc. Connect the points of intersection. This will form an isosceles triangle. 9 E 10 11 12 A P C D B A D B C A T C D A B B M C 13 14 15 16 A A B A A D D C D D B C C B C B 5-7 Constructions 25
Chapter Review (pages 84–85) Note: Since there are many variations of proofs, the following is simply one set of acceptable statements to complete each proof. Depending on the textbook used, the wording and format of reasons may differ, so they have not been supplied for the method of congruence applied in each problem. (These solutions are intended to be used as a guide—other possible solutions may vary.) 1 1. −−− MN bisects PNQ. 2. RND RNQ 3. RNP RQN 4. −−− RN −−− RN 5. RPN RQN (ASA ASA) 2 1. −− PQ −− PR 2. −− QT is a median. 3. −− PT −− RT 4. −− RS is a median. 5. −− PS −− QS 6. PQT PRS (SSS SSS) 3 1. 3 4 2. −− DE −− DF 3. −−− DC −−− DC 4. DEC DFC (SAS SAS) 5. DCE DCF (Corresponding parts of congruent triangles are congruent.) 6. EDC FDC 7. mCAD m1 mEDC mDCE 180 8. mCBD m2 mFDC mDCF 180 9. mCAD mCBD 10. CAD CBD 11. ABC is isosceles. (Definition of isosceles triangle) 4 1. ABC is an equilateral triangle. 2. ___ AB ___ AC (Definition of equilateral triangle) 3. DCB DBC 4. DB DC 5. ___ AD ___ AD 6. ABD ACD (SSS SSS) 7. BAD CAD (Corresponding parts of congruent triangles are congruent.) 8. −−− AD bisects BAC. (Definition of an angle bisector) 26 Chapter 5: Congruence Based on Triangles 5 1. ____ TM ___ TA 2. MTA is isosceles. (Definition of isosceles triangle) 3. ___ TH bisects MTA. 4. ___ TH is an altitude (In an isosceles of MTA. triangle, the bisector is the altitude.) 6 1. ___ AB ___ AD 2. ___ CB ___ CD 3. ___ AC ___ AC 4. ABC ADC (SSS SSS) 5. BAE DAE (Corresponding parts of congruent triangles are congruent) 6. ___ AE ___ AE 7. ABE ADE (ASA ASA) 8. ___ BE ___ DE 9. DAB is isoceles. (Definition of isosceles triangle) 10. ___ AE is the median (Definition of of DAB. median) 11. ___ AE is the altitude (In an isosceles triof DAB. angle, the median is the altitude.) 7 1. ___ AB ___ BD 2. A D 3. DBA CBE 4. EBD EBD 5. DBA EBD CBE EBD 6. EBA CBD 7. ABE DBC (ASA ASA) 8 1. ADE BDC 2. EDB EDB 3. ADE EDB BDC EDB 4. ADB EDC 5. DAE DEC 6. ___ DA ___ DE 7. DAB DEC (ASA ASA) 9 1. 1 2 2. 3 4 3. ___ DE ___ DF 4. DEG DFH (ASA ASA) 5. ___ GD ____ HD (Corresponding parts of congruent triangles are congruent.) 6. EDF EDF
Page 1 and 2: ANSWER KEY Preparing for the REGENT
Page 3 and 4: Contents Chapter 1: Essentials of G
Page 5 and 6: 1-4 Angles (pages 9-10) 1 (4) It is
Page 7 and 8: 6 True 7 True 8 True 9 True 10 Answ
Page 9 and 10: 3 1. e ∨ ~f 2. ~f → g 3. ~e 4.
Page 11 and 12: CHAPTER 3 3-1 Inductive Reasoning (
Page 13 and 14: 6. BAC DAE 6. Transitive property.
Page 15 and 16: CHAPTER 4-1 Setting Up a Valid Proo
Page 17 and 18: 6 Given: BA bisects CBE 1 2 2 4
Page 19 and 20: 1 1. −−−− ABCD 2. 1 2 3. _
Page 21 and 22: 18 1. I is the midpoint of −− E
Page 23 and 24: 5-3 Isosceles and Equilateral Trian
Page 25 and 26: 12. −−− HG −−− DC 13.
Page 27: 5 1. −− FG is the perpendicular
Page 31 and 32: 20 Use constructing congruent angle
Page 33 and 34: 6-3 Line Reflections and Symmetry (
Page 35 and 36: 11 A(0, 8), B(2, 2), C(6, 4) (8) 10
Page 37 and 38: 5 (3) (x, y) → (x, 2y) 6 (1) tran
Page 39 and 40: 11. mABC mADC 12. 2mABD 2mADB 13.
Page 41 and 42: 6. mDAB mCAD mDCB mACD 7. mCAB
Page 43 and 44: g e 17 a _ f d b Undefined c a _
Page 45 and 46: 5 BIG is isosceles because it has t
Page 47 and 48: ___ 27 a M KA (5, 1), M ___ AT (4
Page 49 and 50: 8 106 9 mA 75, mC 67 10 57 11 60
Page 51 and 52: 9-5 The Sum of the Measures of the
Page 53 and 54: 9-7 The Converse of the Isosceles T
Page 55 and 56: 12 1. ___ CE ___ BA , ___ BD ___
Page 57 and 58: 12 a mx 45, my 45 b mx 98, my 8
Page 59 and 60: Quadrilaterals 10-2 The Parallelogr
Page 61 and 62: 7. MAD RCB 8. MAD RCB (SAS SAS)
Page 63 and 64: 5. RSQ TSV (Vertical angles) 6. QR
Page 65 and 66: 3 4x 2 3x 3 x 5 RS 18 4 Perime
Page 67 and 68: Note: Since there are many variatio
Page 69 and 70: 28 Enclose PAT in a large rectangle
Page 71 and 72: Geometry of Three Dimensions 11-1 P
Page 73 and 74: 11-6 Volume of a Prism (pages 269-2
Page 75 and 76: 14 47.5 in. 2 15 h 4 in. 16 25 cm
Page 77 and 78: 14 a 3 : 2 b QR 10, RS 20, ST 12
Page 79 and 80:
4. A A 5. ADE ABC b (AA) AC _ AB
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12 7 √ 2 13 4 14 5 √ 3 15 x
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13-2 Arcs and Chords (pages 350-351
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27 1. Common external tangents, −
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8. mHCT 1 _ m 2 TH mCHT 1 _ CT 2
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16 a (2 √ 2 , 2 √ 2 ), (2 √
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15 a Use constructing a congruent a
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5 Two horizontal lines y 11 and y
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Each review has a total of 58 possi
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Part III For each question, use the
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Chapters 1-3 (pages 438-441) Part I
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Part IV For each question, use the
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16 Score Explanation 4 a 91, b 35
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20 Score Explanation 6 The followin
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Part II For each question, use the
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Part III For each question, use the
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12 Score Explanation 2 31, and an a
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16 Score Explanation 4 DN √ 106
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20 Score Explanation 2 a 3, and an
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17 Score Explanation 4 6 √ 5 , a
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16 Score Explanation 4 mADE 93, mB
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20 Score Explanation Chapters 1-14
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Practice Regents Examination One (p
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36 Score Explanation 4 36, and an a
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32 Score Explanation 2 108, and an
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Part II For each question, use the
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